As the long term goal of this work is to support precision tests of the Standard Model, here we highlight the potential for improved precision from nucleon matrix elements in lattice QCD. Following the work of Ref. [1]}, in Fig. REF (a) we show the constraint on the \(\epsilon _S-\epsilon _T\)  plane assuming perfect knowledge of the nucleon matrix elements. These current best constraints on scalar and tensor interactions arise from \(0^+\rightarrow 0^+\)  nuclear beta decays and radioactive pion decay, which is shown by the green band [1]}, [3]}. The neutron constraints are future projections at the \(10^{-3}\)  level, derived from Eq. REF  and Eq. REF , shown by the red and blue bands in Fig. REF (a). For a more realistic constraint, including the hadronic uncertainties, in Fig.  REF (b) we show the corresponding figure including our best-estimates from the preliminary results reported here for \(g_S\)  and \(g_T\) . When accounting for uncertainties in these lattice QCD calculations, the boundaries on the bands in Fig. REF (b) become wider and contraining power is lost. In order to fully utilise the constraining power of future \(10^{-3}\)  experiments, understanding the lattice-QCD estimates of the tensor and scalar charge at the level of 10% is required  [1]}.
